Yeah, you could do this with little no concerns to the amp itself.
What two pairs of cans were you thinking of connecting? You'll want to keep in mind that one of the 1/4" TRS outputs is for higher impedance headphones while the other is for low impedance.
I'm also not sure if the balanced and unbalanced run simultaneously.
You could always just grab a Y-splitter adapter and use just about any solid amp to the same effect as well. At the end of the day, you're decreasing the impedance load the amp sees, and tapping into the same total power capacity as well, whether it's the Cayin or your existing amp. The Cayin has plenty of juice for driving two headphones at listening levels.